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Block #1,630,871

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/16/2016, 8:24:50 AM Β· Difficulty 10.6068 Β· 5,206,049 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
50ad47a9963863d2ef91a0906420a3109d380485edab406bff74c3ebadc76418
View on Chainz β†—

Height

#1,630,871

Difficulty

10.606787

Transactions

1

Size

201 B

Version

2

Bits

0a9b565d

Nonce

296,792,949

Timestamp

6/16/2016, 8:24:50 AM

Confirmations

5,206,049

Mined by

⛏️ P2SHAGz3WHcLXCJH7WEgmeANBAbm6HSwgBv38o

Merkle Root

5780c920e3514516b19f9ef5c175715ca9de694f1e590f3bee27b6d0f8dc415c
Transactions (1)
Coinbase5780c920e35145…27b6d0f8dc415c
1 in β†’ 1 out8.8700 XPM109 B
AGz3WHcL…SwgBv38o
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.

2.878 Γ— 10⁹⁸(99-digit number)
28781609490174317588…75727274801090396159
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
2.878 Γ— 10⁹⁸(99-digit number)
28781609490174317588…75727274801090396159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.878 Γ— 10⁹⁸(99-digit number)
28781609490174317588…75727274801090396161
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
5.756 Γ— 10⁹⁸(99-digit number)
57563218980348635177…51454549602180792319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.756 Γ— 10⁹⁸(99-digit number)
57563218980348635177…51454549602180792321
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
1.151 Γ— 10⁹⁹(100-digit number)
11512643796069727035…02909099204361584639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.151 Γ— 10⁹⁹(100-digit number)
11512643796069727035…02909099204361584641
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
2.302 Γ— 10⁹⁹(100-digit number)
23025287592139454070…05818198408723169279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.302 Γ— 10⁹⁹(100-digit number)
23025287592139454070…05818198408723169281
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
4.605 Γ— 10⁹⁹(100-digit number)
46050575184278908141…11636396817446338559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.605 Γ— 10⁹⁹(100-digit number)
46050575184278908141…11636396817446338561
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:57,939,655 XPMΒ·at block #6,836,919 Β· updates every 60s
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