Block #2,107,046

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/8/2017, 6:32:54 PM · Difficulty 10.8925 · 4,734,927 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

45cc7584bc480ca991c5dbf1c06b8090a886206872a5340046cad588c6ed47dd

View on Chainz ↗

Height

#2,107,046

Difficulty

10.892455

Transactions

Size

1.94 KB

Version

Bits

0ae477e8

Nonce

1,129,135,081

Timestamp

5/8/2017, 6:32:54 PM

Confirmations

4,734,927

Mined by

⛏️ P2SHALYBAkUvgE6fwCCQZy3MCfqmecGEKByKT6

Merkle Root

633446720259d8f44c73d0ba44708884bbc01b0e44f2783f21fca0f41bbc7b5c

Transactions (3)

Coinbase77e51b0284022f…a980cd0795b90a

1 in → 1 out9.0300 XPM109 B

ALYBAkUv…GEKByKT6

d3a0b44af71ea7…cebf9b464cea72

1 in → 2 out14999.9900 XPM227 B

ARXKmL7f…U1eAxK4X AMRycWoF…13hkF5ou

c97ca555530e77…86c228d7c5b875

10 in → 2 out115.4523 XPM1.52 KB

AGwPVBi4…1Tijs1dg AFpHJhDK…hyA1PvSQ

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.

5.075 × 10⁹⁴(95-digit number)

50751865746148735915…09922016922731519999

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

5.075 × 10⁹⁴(95-digit number)

50751865746148735915…09922016922731519999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.075 × 10⁹⁴(95-digit number)

50751865746148735915…09922016922731520001

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

1.015 × 10⁹⁵(96-digit number)

10150373149229747183…19844033845463039999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.015 × 10⁹⁵(96-digit number)

10150373149229747183…19844033845463040001

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

2.030 × 10⁹⁵(96-digit number)

20300746298459494366…39688067690926079999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.030 × 10⁹⁵(96-digit number)

20300746298459494366…39688067690926080001

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

4.060 × 10⁹⁵(96-digit number)

40601492596918988732…79376135381852159999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.060 × 10⁹⁵(96-digit number)

40601492596918988732…79376135381852160001

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

8.120 × 10⁹⁵(96-digit number)

81202985193837977465…58752270763704319999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.120 × 10⁹⁵(96-digit number)

81202985193837977465…58752270763704320001

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

1.624 × 10⁹⁶(97-digit number)

16240597038767595493…17504541527408639999

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 #2,107,046

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