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Block #2,727,905

TWNLength 12β˜…β˜…β˜…β˜…β˜†

Bi-Twin Chain Β· Discovered 6/30/2018, 9:10:10 AM Β· Difficulty 11.6264 Β· 4,113,252 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
171ded0d04df45f7f97d56e8341f19e4f27bad6b1be6aa96281bf2a6fbf625cd
View on Chainz β†—

Height

#2,727,905

Difficulty

11.626432

Transactions

2

Size

722 B

Version

2

Bits

0ba05dd2

Nonce

967,963,568

Timestamp

6/30/2018, 9:10:10 AM

Confirmations

4,113,252

Mined by

⛏️ P2SHAHVDe3NkGEJeJSJAHKbAoWVcvGaHcpKQ56

Merkle Root

7a215339477c8f9ac6a86fcd7d362e07d1cbf8383af058a123e6d504fe3460fc
Transactions (2)
Coinbase2e4d1f0e72f26d…fcaa3ca292469f
1 in β†’ 1 out7.4000 XPM110 B
AHVDe3Nk…aHcpKQ56
1a32131a91eed4…87c79c11f3aeda
3 in β†’ 2 out541.7344 XPM522 B
AQmjqzoU…5U6sbve9Aaf9ZoEr…CoVWCY1E
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

5.984 Γ— 10⁹³(94-digit number)
59841256225895217258…32140471686493249849
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
5.984 Γ— 10⁹³(94-digit number)
59841256225895217258…32140471686493249849
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.984 Γ— 10⁹³(94-digit number)
59841256225895217258…32140471686493249851
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
1.196 Γ— 10⁹⁴(95-digit number)
11968251245179043451…64280943372986499699
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.196 Γ— 10⁹⁴(95-digit number)
11968251245179043451…64280943372986499701
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
2.393 Γ— 10⁹⁴(95-digit number)
23936502490358086903…28561886745972999399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.393 Γ— 10⁹⁴(95-digit number)
23936502490358086903…28561886745972999401
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
4.787 Γ— 10⁹⁴(95-digit number)
47873004980716173806…57123773491945998799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.787 Γ— 10⁹⁴(95-digit number)
47873004980716173806…57123773491945998801
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
9.574 Γ— 10⁹⁴(95-digit number)
95746009961432347613…14247546983891997599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.574 Γ— 10⁹⁴(95-digit number)
95746009961432347613…14247546983891997601
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
1.914 Γ— 10⁹⁡(96-digit number)
19149201992286469522…28495093967783995199
Verify on FactorDB β†—Wolfram Alpha β†—
2^5 Γ— origin + 1
1.914 Γ— 10⁹⁡(96-digit number)
19149201992286469522…28495093967783995201
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^5 Γ— origin + 1 βˆ’ 2^5 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 12 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜…β˜…β˜†
Rarity
ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,973,620 XPMΒ·at block #6,841,156 Β· updates every 60s
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