Block #911,263

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/26/2015, 11:10:31 PM · Difficulty 10.9316 · 5,898,989 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

dbfaf34d5e71ed0547532a03c0308b9a30ddc8a5eff5ca6e407c1dd2af6d43dd

View on Chainz ↗

Height

#911,263

Difficulty

10.931587

Transactions

Size

2.45 KB

Version

Bits

0aee7c80

Nonce

1,778,128,395

Timestamp

1/26/2015, 11:10:31 PM

Confirmations

5,898,989

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

c48386953e1321dce70212acd76be8a346c74b76a8a18156f249f0473ef70dd3

Transactions (2)

Coinbased23dcd894fcca0…b2fb3f7b11636b

1 in → 1 out8.3800 XPM116 B

ANSXnLY2…Sd25TjkD

5d5adc70e70892…59b1f837ac8af7

15 in → 2 out1179.4988 XPM2.24 KB

Ac3Nuu5f…pwZACyFP AQ3SuyCM…AmNvneTb

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.

7.032 × 10⁹⁵(96-digit number)

70323606158874702930…90290366379038662399

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

7.032 × 10⁹⁵(96-digit number)

70323606158874702930…90290366379038662399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.032 × 10⁹⁵(96-digit number)

70323606158874702930…90290366379038662401

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

1.406 × 10⁹⁶(97-digit number)

14064721231774940586…80580732758077324799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.406 × 10⁹⁶(97-digit number)

14064721231774940586…80580732758077324801

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

2.812 × 10⁹⁶(97-digit number)

28129442463549881172…61161465516154649599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.812 × 10⁹⁶(97-digit number)

28129442463549881172…61161465516154649601

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

5.625 × 10⁹⁶(97-digit number)

56258884927099762344…22322931032309299199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.625 × 10⁹⁶(97-digit number)

56258884927099762344…22322931032309299201

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

1.125 × 10⁹⁷(98-digit number)

11251776985419952468…44645862064618598399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.125 × 10⁹⁷(98-digit number)

11251776985419952468…44645862064618598401

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 #911,263

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