Block #922,431

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/4/2015, 11:38:52 AM · Difficulty 10.9153 · 5,873,746 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

de868f7cd169d1956c693098aebeb1f09e7157853ba4aab5df9fab4ef7cbf982

View on Chainz ↗

Height

#922,431

Difficulty

10.915310

Transactions

Size

116.02 KB

Version

Bits

0aea51c7

Nonce

28,316,160

Timestamp

2/4/2015, 11:38:52 AM

Confirmations

5,873,746

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

41d5edf1cb63e42f13140a1ea7869b0cfd9f9e8630dd6aca7819718286ad0c77

Transactions (5)

Coinbase97cfaf7fe2c597…c3e077cc0b387a

1 in → 1 out9.5800 XPM116 B

ANSXnLY2…Sd25TjkD

3656f1378856c3…5f3f4931b5b325

200 in → 1 out1079.5009 XPM28.96 KB

AKuP4XsJ…owbodNxQ

be0b6e7acf7102…7f140c832b53fd

200 in → 1 out1018.8776 XPM28.95 KB

AKuP4XsJ…owbodNxQ

bb67981a0f0a6d…c75d12b6bfeb53

200 in → 1 out999.4276 XPM28.95 KB

AKuP4XsJ…owbodNxQ

d1efa6337f75c9…a62fb2c2389d98

200 in → 1 out994.3344 XPM28.95 KB

AKuP4XsJ…owbodNxQ

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.

9.451 × 10⁹⁸(99-digit number)

94512503061364267249…59526149847468605439

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

9.451 × 10⁹⁸(99-digit number)

94512503061364267249…59526149847468605439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.451 × 10⁹⁸(99-digit number)

94512503061364267249…59526149847468605441

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

1.890 × 10⁹⁹(100-digit number)

18902500612272853449…19052299694937210879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.890 × 10⁹⁹(100-digit number)

18902500612272853449…19052299694937210881

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

3.780 × 10⁹⁹(100-digit number)

37805001224545706899…38104599389874421759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.780 × 10⁹⁹(100-digit number)

37805001224545706899…38104599389874421761

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

7.561 × 10⁹⁹(100-digit number)

75610002449091413799…76209198779748843519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.561 × 10⁹⁹(100-digit number)

75610002449091413799…76209198779748843521

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

1.512 × 10¹⁰⁰(101-digit number)

15122000489818282759…52418397559497687039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.512 × 10¹⁰⁰(101-digit number)

15122000489818282759…52418397559497687041

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