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Block #2,054,336

TWNLength 12β˜…β˜…β˜…β˜…β˜†

Bi-Twin Chain Β· Discovered 4/4/2017, 10:36:00 AM Β· Difficulty 10.7915 Β· 4,788,755 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
86527be5e45fc5b5dfb5b341c222b4bf3957dd5f5f28ccb0103d222c1ecb7221
View on Chainz β†—

Height

#2,054,336

Difficulty

10.791496

Transactions

1

Size

200 B

Version

2

Bits

0aca9f73

Nonce

44,621,330

Timestamp

4/4/2017, 10:36:00 AM

Confirmations

4,788,755

Mined by

⛏️ P2SHAUTt8dEyDhmrGSMcN5BCiJv9zMjgMf8tWE

Merkle Root

67b8ea66337e79bfdaa6d314b3dd8562cc1e1f3a7cfa5f6e0c7aa7a02bfddc71
Transactions (1)
Coinbase67b8ea66337e79…7aa7a02bfddc71
1 in β†’ 1 out8.5700 XPM110 B
AUTt8dEy…jgMf8tWE
Prime Chain Origin

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

1.372 Γ— 10⁹⁡(96-digit number)
13726329388636322718…57298899795124007999
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— 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 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
1.372 Γ— 10⁹⁡(96-digit number)
13726329388636322718…57298899795124007999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.372 Γ— 10⁹⁡(96-digit number)
13726329388636322718…57298899795124008001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
2.745 Γ— 10⁹⁡(96-digit number)
27452658777272645436…14597799590248015999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.745 Γ— 10⁹⁡(96-digit number)
27452658777272645436…14597799590248016001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
5.490 Γ— 10⁹⁡(96-digit number)
54905317554545290872…29195599180496031999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.490 Γ— 10⁹⁡(96-digit number)
54905317554545290872…29195599180496032001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
1.098 Γ— 10⁹⁢(97-digit number)
10981063510909058174…58391198360992063999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.098 Γ— 10⁹⁢(97-digit number)
10981063510909058174…58391198360992064001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
2.196 Γ— 10⁹⁢(97-digit number)
21962127021818116348…16782396721984127999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.196 Γ— 10⁹⁢(97-digit number)
21962127021818116348…16782396721984128001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
4.392 Γ— 10⁹⁢(97-digit number)
43924254043636232697…33564793443968255999
Verify on FactorDB β†—Wolfram Alpha β†—
2^5 Γ— origin + 1
4.392 Γ— 10⁹⁢(97-digit number)
43924254043636232697…33564793443968256001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^5 Γ— origin + 1 βˆ’ 2^5 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 12 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜…β˜…β˜†
Rarity
ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” 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 βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
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