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Block #1,340,903

TWNLength 10ā˜…ā˜…ā˜†ā˜†ā˜†

Bi-Twin Chain Ā· Discovered 11/25/2015, 10:06:55 AM Ā· Difficulty 10.8024 Ā· 5,463,913 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e2422c7a6145e0d11f35260459fbf1c1b3ec1fba344fcb0f90492dbb17d13125
View on Chainz ā†—

Height

#1,340,903

Difficulty

10.802432

Transactions

2

Size

1.11 KB

Version

2

Bits

0acd6c2f

Nonce

51,687,605

Timestamp

11/25/2015, 10:06:55 AM

Confirmations

5,463,913

Mined by

ā›ļø P2SHAXwhebPRaKPo7GQearZ6GwB9LAAU5yhegt

Merkle Root

1adcccf9219aeca0c31174dc6c5f1f127657ce6e2b65f1d9d2358551b627fc1d
Transactions (2)
Coinbase59dd797e16a507ā€¦1d3fcb5e9aace4
1 in ā†’ 1 out8.5700 XPM109 B
AXwhebPRā€¦AU5yhegt
8b35984164fefcā€¦e631bc4122aafb
1 in ā†’ 23 out2.4536 XPM940 B
AN1c5SkYā€¦LEhEtG4iAT9ngrHaā€¦L1nnNKSXAPi5bJTiā€¦HVjutVe5AZX7v6cNā€¦acaWmkvrAaz5e4Noā€¦k2jB8pfE
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) ā€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

2.244 Ɨ 10ā¹āµ(96-digit number)
22448601287804478883ā€¦33344506731267928639
Discovered Prime Numbers
Lower: 2^k Ɨ origin āˆ’ 1 | Upper: 2^k Ɨ 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 ā€” Twin Prime Pair (origin Ā± 1)
origin āˆ’ 1
2.244 Ɨ 10ā¹āµ(96-digit number)
22448601287804478883ā€¦33344506731267928639
Verify on FactorDB ā†—Wolfram Alpha ā†—
origin + 1
2.244 Ɨ 10ā¹āµ(96-digit number)
22448601287804478883ā€¦33344506731267928641
Verify on FactorDB ā†—Wolfram Alpha ā†—
Difference: origin + 1 āˆ’ origin āˆ’ 1 = 2 (twin primes āœ“)
Level 1 ā€” Twin Prime Pair (2^1 Ɨ origin Ā± 1)
2^1 Ɨ origin āˆ’ 1
4.489 Ɨ 10ā¹āµ(96-digit number)
44897202575608957766ā€¦66689013462535857279
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^1 Ɨ origin + 1
4.489 Ɨ 10ā¹āµ(96-digit number)
44897202575608957766ā€¦66689013462535857281
Verify on FactorDB ā†—Wolfram Alpha ā†—
Difference: 2^1 Ɨ origin + 1 āˆ’ 2^1 Ɨ origin āˆ’ 1 = 2 (twin primes āœ“)
Level 2 ā€” Twin Prime Pair (2^2 Ɨ origin Ā± 1)
2^2 Ɨ origin āˆ’ 1
8.979 Ɨ 10ā¹āµ(96-digit number)
89794405151217915532ā€¦33378026925071714559
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^2 Ɨ origin + 1
8.979 Ɨ 10ā¹āµ(96-digit number)
89794405151217915532ā€¦33378026925071714561
Verify on FactorDB ā†—Wolfram Alpha ā†—
Difference: 2^2 Ɨ origin + 1 āˆ’ 2^2 Ɨ origin āˆ’ 1 = 2 (twin primes āœ“)
Level 3 ā€” Twin Prime Pair (2^3 Ɨ origin Ā± 1)
2^3 Ɨ origin āˆ’ 1
1.795 Ɨ 10ā¹ā¶(97-digit number)
17958881030243583106ā€¦66756053850143429119
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^3 Ɨ origin + 1
1.795 Ɨ 10ā¹ā¶(97-digit number)
17958881030243583106ā€¦66756053850143429121
Verify on FactorDB ā†—Wolfram Alpha ā†—
Difference: 2^3 Ɨ origin + 1 āˆ’ 2^3 Ɨ origin āˆ’ 1 = 2 (twin primes āœ“)
Level 4 ā€” Twin Prime Pair (2^4 Ɨ origin Ā± 1)
2^4 Ɨ origin āˆ’ 1
3.591 Ɨ 10ā¹ā¶(97-digit number)
35917762060487166212ā€¦33512107700286858239
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^4 Ɨ origin + 1
3.591 Ɨ 10ā¹ā¶(97-digit number)
35917762060487166212ā€¦33512107700286858241
Verify on FactorDB ā†—Wolfram Alpha ā†—
Difference: 2^4 Ɨ origin + 1 āˆ’ 2^4 Ɨ origin āˆ’ 1 = 2 (twin primes āœ“)

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 ā€” the large number shown above ā€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

ā˜…ā˜…ā˜†ā˜†ā˜†
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 Ɨ 3 Ɨ 5 Ɨ 7 Ɨ ā€¦), the result is the first prime in the chain. The origin is deliberately divisible by this primorial ā€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Ɨ Primorial (2Ā·3Ā·5Ā·7Ā·11Ā·ā€¦)
Source: Primecoin prime.cpp ā€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors ā€” 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 āˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,682,597 XPMĀ·at block #6,804,815 Ā· updates every 60s
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