Block #420,714

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/26/2014, 1:25:13 PM · Difficulty 10.3744 · 6,388,820 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ce456f9d56ab1f6523eea29a2c17e5f8ad52552080e6cae008c4315542787000

View on Chainz ↗

Height

#420,714

Difficulty

10.374381

Transactions

Size

881 B

Version

Bits

0a5fd768

Nonce

114,982

Timestamp

2/26/2014, 1:25:13 PM

Confirmations

6,388,820

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

2302ac7597fe9775946d582f1f84033e8b9382a353005ee974b5cf1770405f45

Transactions (4)

Coinbase1d3c69d0dcefc4…3445b8a07503bb

1 in → 1 out9.3100 XPM110 B

AeKNrjNj…1NEq95Ta

02a5d042aa4950…5001dfd7b959be

1 in → 2 out6.1449 XPM226 B

AGyXXxoB…1CBDrnAK AafXBxi8…MTbj7rvU

b46bfa4afce473…999b80d1213a2f

1 in → 2 out4.1111 XPM225 B

AVVvVC2v…ByPnMRtd AanoyEFy…qBa8pWDn

3300a3f1b7793e…de6f0723a316cb

1 in → 2 out6.1553 XPM227 B

AMu5m5Dd…eCCDovnm AV5GFPHg…MHg58A4X

Prime Chain Origin

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

4.594 × 10¹⁰¹(102-digit number)

45944218271186467307…30678585718745366399

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × 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 — Twin Prime Pair (origin ± 1)

origin − 1

4.594 × 10¹⁰¹(102-digit number)

45944218271186467307…30678585718745366399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.594 × 10¹⁰¹(102-digit number)

45944218271186467307…30678585718745366401

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

9.188 × 10¹⁰¹(102-digit number)

91888436542372934615…61357171437490732799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.188 × 10¹⁰¹(102-digit number)

91888436542372934615…61357171437490732801

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

1.837 × 10¹⁰²(103-digit number)

18377687308474586923…22714342874981465599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.837 × 10¹⁰²(103-digit number)

18377687308474586923…22714342874981465601

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

3.675 × 10¹⁰²(103-digit number)

36755374616949173846…45428685749962931199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.675 × 10¹⁰²(103-digit number)

36755374616949173846…45428685749962931201

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

7.351 × 10¹⁰²(103-digit number)

73510749233898347692…90857371499925862399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.351 × 10¹⁰²(103-digit number)

73510749233898347692…90857371499925862401

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★☆☆☆

Rarity

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — 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 − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer

Block #420,714

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