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Block #2,960,516

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 12/10/2018, 10:40:56 PM Β· Difficulty 11.3480 Β· 3,883,520 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
96844e0de76ac5a6cc30d4b770147fbc66a6119c5fe0d17df557e7e7cfc85029
View on Chainz β†—

Height

#2,960,516

Difficulty

11.347982

Transactions

1

Size

201 B

Version

2

Bits

0b59155d

Nonce

638,552,905

Timestamp

12/10/2018, 10:40:56 PM

Confirmations

3,883,520

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

12436686ca085910a321236298d528bf855fbc452b07f33f87af0a3fe41c20d7
Transactions (1)
Coinbase12436686ca0859…af0a3fe41c20d7
1 in β†’ 1 out7.7500 XPM110 B
AbXwmGxD…4XXYP765
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.

6.203 Γ— 10⁹⁷(98-digit number)
62033431034243946409…08610256168948531199
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
6.203 Γ— 10⁹⁷(98-digit number)
62033431034243946409…08610256168948531199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.203 Γ— 10⁹⁷(98-digit number)
62033431034243946409…08610256168948531201
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
1.240 Γ— 10⁹⁸(99-digit number)
12406686206848789281…17220512337897062399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.240 Γ— 10⁹⁸(99-digit number)
12406686206848789281…17220512337897062401
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
2.481 Γ— 10⁹⁸(99-digit number)
24813372413697578563…34441024675794124799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.481 Γ— 10⁹⁸(99-digit number)
24813372413697578563…34441024675794124801
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
4.962 Γ— 10⁹⁸(99-digit number)
49626744827395157127…68882049351588249599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.962 Γ— 10⁹⁸(99-digit number)
49626744827395157127…68882049351588249601
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
9.925 Γ— 10⁹⁸(99-digit number)
99253489654790314254…37764098703176499199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.925 Γ— 10⁹⁸(99-digit number)
99253489654790314254…37764098703176499201
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
1.985 Γ— 10⁹⁹(100-digit number)
19850697930958062850…75528197406352998399
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,996,665 XPMΒ·at block #6,844,035 Β· updates every 60s
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