Block #936,269

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 2/14/2015, 3:28:50 PM · Difficulty 10.9015 · 5,879,789 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cec4574efdedc0f477998cbe05b62108c6f2b8a3ecc047ba2e0ece3ebd6db74e

View on Chainz ↗

Height

#936,269

Difficulty

10.901510

Transactions

Size

2.67 KB

Version

Bits

0ae6c956

Nonce

919,565,473

Timestamp

2/14/2015, 3:28:50 PM

Confirmations

5,879,789

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

777863131a4c0e4a5dc7f92a3a50ca18f65ae1eb5cfb5cf4c61ca0b5877668de

Transactions (3)

Coinbase23a516524302da…c8934d181ba29e

1 in → 1 out8.4400 XPM116 B

ANSXnLY2…Sd25TjkD

ac9795047a87b8…fa2b3e839a3308

15 in → 2 out100.1605 XPM2.25 KB

AMj5jjch…yiA2GFBc AH1Porpk…pjuNCGNm

cacef7ff1cb1e3…15347cd20b6d00

1 in → 2 out2.4140 XPM225 B

AKrnLwHd…QTQP7ngM AHRoBSh4…BSVTQ36Q

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.

3.892 × 10⁹⁹(100-digit number)

38928838434240693798…05173563282090229759

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

3.892 × 10⁹⁹(100-digit number)

38928838434240693798…05173563282090229759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.892 × 10⁹⁹(100-digit number)

38928838434240693798…05173563282090229761

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

7.785 × 10⁹⁹(100-digit number)

77857676868481387596…10347126564180459519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.785 × 10⁹⁹(100-digit number)

77857676868481387596…10347126564180459521

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

1.557 × 10¹⁰⁰(101-digit number)

15571535373696277519…20694253128360919039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.557 × 10¹⁰⁰(101-digit number)

15571535373696277519…20694253128360919041

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

3.114 × 10¹⁰⁰(101-digit number)

31143070747392555038…41388506256721838079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.114 × 10¹⁰⁰(101-digit number)

31143070747392555038…41388506256721838081

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

6.228 × 10¹⁰⁰(101-digit number)

62286141494785110077…82777012513443676159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.228 × 10¹⁰⁰(101-digit number)

62286141494785110077…82777012513443676161

Verify on FactorDB ↗Wolfram Alpha ↗

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

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.245 × 10¹⁰¹(102-digit number)

12457228298957022015…65554025026887352319

Verify on FactorDB ↗Wolfram Alpha ↗

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 — 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

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 × 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 #936,269

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