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Block #2,831,635

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/9/2018, 11:25:25 AM Β· Difficulty 11.7175 Β· 4,011,783 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
39907b4863b47872f496b9a0482df70aad67963720cedbc022a0195339fb7965
View on Chainz β†—

Height

#2,831,635

Difficulty

11.717504

Transactions

1

Size

201 B

Version

2

Bits

0bb7ae5c

Nonce

1,088,637,229

Timestamp

9/9/2018, 11:25:25 AM

Confirmations

4,011,783

Mined by

⛏️ P2SHAXGDG51NzhRUb2AWut28v3wFBP7CdMRiCs

Merkle Root

04d5a1d3af778e2982f58e3f9110997e7f38b4c47021497f89c1111f321dc061
Transactions (1)
Coinbase04d5a1d3af778e…c1111f321dc061
1 in β†’ 1 out7.2700 XPM110 B
AXGDG51N…7CdMRiCs
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.

1.991 Γ— 10⁹⁸(99-digit number)
19913689827872845813…63942151835753512959
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
1.991 Γ— 10⁹⁸(99-digit number)
19913689827872845813…63942151835753512959
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.991 Γ— 10⁹⁸(99-digit number)
19913689827872845813…63942151835753512961
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
3.982 Γ— 10⁹⁸(99-digit number)
39827379655745691626…27884303671507025919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.982 Γ— 10⁹⁸(99-digit number)
39827379655745691626…27884303671507025921
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
7.965 Γ— 10⁹⁸(99-digit number)
79654759311491383252…55768607343014051839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.965 Γ— 10⁹⁸(99-digit number)
79654759311491383252…55768607343014051841
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
1.593 Γ— 10⁹⁹(100-digit number)
15930951862298276650…11537214686028103679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.593 Γ— 10⁹⁹(100-digit number)
15930951862298276650…11537214686028103681
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
3.186 Γ— 10⁹⁹(100-digit number)
31861903724596553301…23074429372056207359
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.186 Γ— 10⁹⁹(100-digit number)
31861903724596553301…23074429372056207361
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
6.372 Γ— 10⁹⁹(100-digit number)
63723807449193106602…46148858744112414719
Verify on FactorDB β†—Wolfram Alpha β†—

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 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
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 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:57,991,712 XPMΒ·at block #6,843,417 Β· updates every 60s
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