Block #351,807

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/9/2014, 10:38:26 PM · Difficulty 10.3009 · 6,464,061 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

52687ba46bbc24fbec8d21a0f6a67ae4fa9c7f5f56fe4cd7cc7bc7df3fd08ede

View on Chainz ↗

Height

#351,807

Difficulty

10.300856

Transactions

Size

1.52 KB

Version

Bits

0a4d04e4

Nonce

107,750

Timestamp

1/9/2014, 10:38:26 PM

Confirmations

6,464,061

Mined by

⛏️ P2SHAPtY3ZbPMXAWJKsDRLL2663VqH1FDtytrt

Merkle Root

e04f06624c773c5ac915d58ecceede362b2ce6672116b408c03ce64bc7ab3872

Transactions (5)

Coinbase9b3567ac1bd107…51f226e533a16a

1 in → 1 out9.4500 XPM112 B

APtY3ZbP…1FDtytrt

eab06895d24dc2…c41944478956dd

1 in → 2 out5.4083 XPM227 B

AVMY29Fu…oc4728oj AHVn7ZZK…eciBPRkv

c80cc8eba6b751…a225ef22c969e3

1 in → 2 out6.4110 XPM226 B

AP72CeHo…gigbrk3M AZ9KZa64…5JTTKAB4

0d2e98514666b5…ee9e5689d39714

1 in → 2 out4.3501 XPM227 B

APYgzNAd…NPeTHyqr AL3YAAzD…NtNyZ9Lb

bd4df98739d7c1…27ffbe9c6a9888

4 in → 2 out1.2707 XPM669 B

AdBzDVfj…fwoBBQH4 AGUiHrXX…99nzH74G

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.

2.235 × 10⁹⁹(100-digit number)

22357794996613191364…30333831061672273919

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

2.235 × 10⁹⁹(100-digit number)

22357794996613191364…30333831061672273919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.235 × 10⁹⁹(100-digit number)

22357794996613191364…30333831061672273921

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

4.471 × 10⁹⁹(100-digit number)

44715589993226382729…60667662123344547839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.471 × 10⁹⁹(100-digit number)

44715589993226382729…60667662123344547841

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

8.943 × 10⁹⁹(100-digit number)

89431179986452765458…21335324246689095679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.943 × 10⁹⁹(100-digit number)

89431179986452765458…21335324246689095681

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

1.788 × 10¹⁰⁰(101-digit number)

17886235997290553091…42670648493378191359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.788 × 10¹⁰⁰(101-digit number)

17886235997290553091…42670648493378191361

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

3.577 × 10¹⁰⁰(101-digit number)

35772471994581106183…85341296986756382719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.577 × 10¹⁰⁰(101-digit number)

35772471994581106183…85341296986756382721

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 #351,807

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