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Block #2,634,607

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/28/2018, 11:13:37 PM Β· Difficulty 11.2563 Β· 4,208,889 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f21108b15e204bd9997528822e97f4c205dd4e5f89c4d1a98e60451a1c2a5acb
View on Chainz β†—

Height

#2,634,607

Difficulty

11.256337

Transactions

2

Size

869 B

Version

2

Bits

0b419f4c

Nonce

1,087,451,917

Timestamp

4/28/2018, 11:13:37 PM

Confirmations

4,208,889

Mined by

⛏️ P2SHAU76t8NXG6tMCm9qH8asz2Vajg3tAT1Uj2

Merkle Root

ec5582f3761a03b89d5a8388ae7644c292d6917cd3431d98aeed9d16b60680f2
Transactions (2)
Coinbase48c60e04657408…67810357bafca8
1 in β†’ 1 out7.8900 XPM109 B
AU76t8NX…3tAT1Uj2
e294214224203a…d860ffbfecfd95
4 in β†’ 2 out15.6752 XPM670 B
AZ4UnHzJ…PH7NQioAAYZequ6U…7NokG9do
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.

2.123 Γ— 10⁹⁡(96-digit number)
21233242595185959475…18743377416563506679
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
2.123 Γ— 10⁹⁡(96-digit number)
21233242595185959475…18743377416563506679
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.123 Γ— 10⁹⁡(96-digit number)
21233242595185959475…18743377416563506681
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
4.246 Γ— 10⁹⁡(96-digit number)
42466485190371918950…37486754833127013359
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.246 Γ— 10⁹⁡(96-digit number)
42466485190371918950…37486754833127013361
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
8.493 Γ— 10⁹⁡(96-digit number)
84932970380743837900…74973509666254026719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.493 Γ— 10⁹⁡(96-digit number)
84932970380743837900…74973509666254026721
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
1.698 Γ— 10⁹⁢(97-digit number)
16986594076148767580…49947019332508053439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.698 Γ— 10⁹⁢(97-digit number)
16986594076148767580…49947019332508053441
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
3.397 Γ— 10⁹⁢(97-digit number)
33973188152297535160…99894038665016106879
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.397 Γ— 10⁹⁢(97-digit number)
33973188152297535160…99894038665016106881
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
6.794 Γ— 10⁹⁢(97-digit number)
67946376304595070320…99788077330032213759
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
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