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Block #827,692

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/25/2014, 5:33:52 PM Β· Difficulty 10.9778 Β· 5,978,624 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b8772213808617dc93f530b41fb3a5575a1b8f0d8bcc3ff80203b55b6eb19642
View on Chainz β†—

Height

#827,692

Difficulty

10.977816

Transactions

2

Size

425 B

Version

2

Bits

0afa5228

Nonce

964,126,250

Timestamp

11/25/2014, 5:33:52 PM

Confirmations

5,978,624

Mined by

⛏️ P2SHAVx68HgYH5S2SKgAR1BNkUGoBfGft1djdV

Merkle Root

980caec6777f55b4537713eddf2e515d443a707307b34f36bf938542d8ebc192
Transactions (2)
Coinbasea60a2ccb0498eb…a2b2f5a82c8516
1 in β†’ 1 out8.2900 XPM109 B
AVx68HgY…Gft1djdV
ce99022d897f9b…3869751129297b
1 in β†’ 2 out2.0644 XPM226 B
ALNQaD7f…2g74yYvVAUzWY5XK…N7JTbEmj
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.

8.248 Γ— 10⁹⁴(95-digit number)
82483559178211817722…07848734635018868479
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
8.248 Γ— 10⁹⁴(95-digit number)
82483559178211817722…07848734635018868479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.248 Γ— 10⁹⁴(95-digit number)
82483559178211817722…07848734635018868481
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
1.649 Γ— 10⁹⁡(96-digit number)
16496711835642363544…15697469270037736959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.649 Γ— 10⁹⁡(96-digit number)
16496711835642363544…15697469270037736961
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
3.299 Γ— 10⁹⁡(96-digit number)
32993423671284727089…31394938540075473919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.299 Γ— 10⁹⁡(96-digit number)
32993423671284727089…31394938540075473921
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
6.598 Γ— 10⁹⁡(96-digit number)
65986847342569454178…62789877080150947839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.598 Γ— 10⁹⁡(96-digit number)
65986847342569454178…62789877080150947841
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
1.319 Γ— 10⁹⁢(97-digit number)
13197369468513890835…25579754160301895679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.319 Γ— 10⁹⁢(97-digit number)
13197369468513890835…25579754160301895681
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

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 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
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 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
Circulating Supply:57,694,609 XPMΒ·at block #6,806,315 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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