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Block #891,401

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/11/2015, 7:16:32 PM Β· Difficulty 10.9533 Β· 5,935,220 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
765b28a5a84f70c4ef404883ce102eba13bb69acac7d4adf6a0aa29bcb9d9d78
View on Chainz β†—

Height

#891,401

Difficulty

10.953251

Transactions

1

Size

206 B

Version

2

Bits

0af4083b

Nonce

1,445,071,986

Timestamp

1/11/2015, 7:16:32 PM

Confirmations

5,935,220

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

6998abf244955c5c9c5971cca431fed277931ca4cd8f433c75d12e056a8b5b9e
Transactions (1)
Coinbase6998abf244955c…d12e056a8b5b9e
1 in β†’ 1 out8.3200 XPM116 B
ANSXnLY2…Sd25TjkD
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.

5.289 Γ— 10⁹⁡(96-digit number)
52898651147770626240…94050563557243873839
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
5.289 Γ— 10⁹⁡(96-digit number)
52898651147770626240…94050563557243873839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.289 Γ— 10⁹⁡(96-digit number)
52898651147770626240…94050563557243873841
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
1.057 Γ— 10⁹⁢(97-digit number)
10579730229554125248…88101127114487747679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.057 Γ— 10⁹⁢(97-digit number)
10579730229554125248…88101127114487747681
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
2.115 Γ— 10⁹⁢(97-digit number)
21159460459108250496…76202254228975495359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.115 Γ— 10⁹⁢(97-digit number)
21159460459108250496…76202254228975495361
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
4.231 Γ— 10⁹⁢(97-digit number)
42318920918216500992…52404508457950990719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.231 Γ— 10⁹⁢(97-digit number)
42318920918216500992…52404508457950990721
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
8.463 Γ— 10⁹⁢(97-digit number)
84637841836433001984…04809016915901981439
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.463 Γ— 10⁹⁢(97-digit number)
84637841836433001984…04809016915901981441
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:57,857,121 XPMΒ·at block #6,826,620 Β· updates every 60s
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