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Block #2,647,016

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/3/2018, 4:16:08 PM Β· Difficulty 11.7567 Β· 4,194,963 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
062828a1d633d7d0ba85b0d9b0a5b707a51611ff19b7164b4b90fd5aaa202a80
View on Chainz β†—

Height

#2,647,016

Difficulty

11.756728

Transactions

2

Size

724 B

Version

2

Bits

0bc1b8e9

Nonce

515,450,478

Timestamp

5/3/2018, 4:16:08 PM

Confirmations

4,194,963

Mined by

⛏️ P2SHAVq3RQU1LShSmuN9osXnE3tzTdPUYNk4TX

Merkle Root

4ea8c176f473bfe6d225a988d1c30a1c2958a12a8d03a9cf2f2cab88bff767c0
Transactions (2)
Coinbase5a502d3a0af788…27019db18da6cd
1 in β†’ 1 out7.2300 XPM110 B
AVq3RQU1…PUYNk4TX
fbeb877e9778d6…3dc8d945227371
3 in β†’ 2 out6.9717 XPM523 B
AdZthKV6…YW6b8e9gAdScb5F1…944URUYG
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.

3.066 Γ— 10⁹⁢(97-digit number)
30663924472834417969…40977572085649735679
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
3.066 Γ— 10⁹⁢(97-digit number)
30663924472834417969…40977572085649735679
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.066 Γ— 10⁹⁢(97-digit number)
30663924472834417969…40977572085649735681
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
6.132 Γ— 10⁹⁢(97-digit number)
61327848945668835939…81955144171299471359
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.132 Γ— 10⁹⁢(97-digit number)
61327848945668835939…81955144171299471361
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
1.226 Γ— 10⁹⁷(98-digit number)
12265569789133767187…63910288342598942719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.226 Γ— 10⁹⁷(98-digit number)
12265569789133767187…63910288342598942721
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
2.453 Γ— 10⁹⁷(98-digit number)
24531139578267534375…27820576685197885439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.453 Γ— 10⁹⁷(98-digit number)
24531139578267534375…27820576685197885441
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
4.906 Γ— 10⁹⁷(98-digit number)
49062279156535068751…55641153370395770879
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.906 Γ— 10⁹⁷(98-digit number)
49062279156535068751…55641153370395770881
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
9.812 Γ— 10⁹⁷(98-digit number)
98124558313070137503…11282306740791541759
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:57,980,217 XPMΒ·at block #6,841,978 Β· updates every 60s
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