Block #1,067,929

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/20/2015, 2:01:21 PM · Difficulty 10.7391 · 5,747,209 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a717582086acd3a6410da2a7cd712baa985009d9ae74570b7f5ff75b343d7b1a

View on Chainz ↗

Height

#1,067,929

Difficulty

10.739099

Transactions

Size

499 B

Version

Bits

0abd3594

Nonce

1,336,633,756

Timestamp

5/20/2015, 2:01:21 PM

Confirmations

5,747,209

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

047b2714efa88ad7b7546ed107cae05e1b46d0c429d9651d1a0887bff388a18d

Transactions (2)

Coinbase4badd91ce78d7f…2112510dbe0a78

1 in → 1 out8.6700 XPM116 B

ANSXnLY2…Sd25TjkD

d2fff63c14ecfa…d825f20d559cd2

1 in → 5 out8.6600 XPM293 B

ALqEZWdP…6VPV6ooe AWVdqMHf…3TnrQBYd ATrgZbVD…smHMiiTk AVvA9Gzu…7fxjvGRS AcQSa8z8…7a65Dx9G

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.

5.300 × 10⁹⁵(96-digit number)

53007897276279619886…90388024621954091519

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

5.300 × 10⁹⁵(96-digit number)

53007897276279619886…90388024621954091519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.300 × 10⁹⁵(96-digit number)

53007897276279619886…90388024621954091521

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

1.060 × 10⁹⁶(97-digit number)

10601579455255923977…80776049243908183039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.060 × 10⁹⁶(97-digit number)

10601579455255923977…80776049243908183041

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

2.120 × 10⁹⁶(97-digit number)

21203158910511847954…61552098487816366079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.120 × 10⁹⁶(97-digit number)

21203158910511847954…61552098487816366081

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

4.240 × 10⁹⁶(97-digit number)

42406317821023695909…23104196975632732159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.240 × 10⁹⁶(97-digit number)

42406317821023695909…23104196975632732161

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

8.481 × 10⁹⁶(97-digit number)

84812635642047391819…46208393951265464319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.481 × 10⁹⁶(97-digit number)

84812635642047391819…46208393951265464321

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 #1,067,929

Cookie Preferences