Block #2,457,250

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/4/2018, 12:46:10 PM · Difficulty 10.9539 · 4,384,257 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6cfc4e9b76c8cc59d6cf75e41ea2d138f47931dde5443591ff106fd404bccdb0

View on Chainz ↗

Height

#2,457,250

Difficulty

10.953948

Transactions

Size

870 B

Version

Bits

0af435ef

Nonce

902,177,421

Timestamp

1/4/2018, 12:46:10 PM

Confirmations

4,384,257

Mined by

⛏️ P2SHAWaXAABzNfJcHVNLUHSLUMpHAtmVC1P8Ze

Merkle Root

74b2840503bd4795d959a7272f8671629928538c2133bb0d97abdd20fa5b671c

Transactions (2)

Coinbasebec8704d31fccb…0123cb48779379

1 in → 1 out8.3300 XPM109 B

AWaXAABz…mVC1P8Ze

0326ead1b0012e…c82f10e537e01e

4 in → 2 out45.6961 XPM670 B

AaNnbBg7…UhjSkdpu AH1td1kC…EFFJGB8d

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.

2.637 × 10⁹⁶(97-digit number)

26373078328395061312…41261971684723916799

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

2.637 × 10⁹⁶(97-digit number)

26373078328395061312…41261971684723916799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.637 × 10⁹⁶(97-digit number)

26373078328395061312…41261971684723916801

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

5.274 × 10⁹⁶(97-digit number)

52746156656790122625…82523943369447833599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.274 × 10⁹⁶(97-digit number)

52746156656790122625…82523943369447833601

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

1.054 × 10⁹⁷(98-digit number)

10549231331358024525…65047886738895667199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.054 × 10⁹⁷(98-digit number)

10549231331358024525…65047886738895667201

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

2.109 × 10⁹⁷(98-digit number)

21098462662716049050…30095773477791334399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.109 × 10⁹⁷(98-digit number)

21098462662716049050…30095773477791334401

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

4.219 × 10⁹⁷(98-digit number)

42196925325432098100…60191546955582668799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.219 × 10⁹⁷(98-digit number)

42196925325432098100…60191546955582668801

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 #2,457,250

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