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Block #1,845,888

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/12/2016, 5:53:49 PM Β· Difficulty 10.6101 Β· 4,997,551 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
502bc8305df42a9a52bc62b9e5c76f5bebaa1b36783bee2d032ec3a8dcea1054
View on Chainz β†—

Height

#1,845,888

Difficulty

10.610092

Transactions

1

Size

201 B

Version

2

Bits

0a9c2eff

Nonce

18,164,236

Timestamp

11/12/2016, 5:53:49 PM

Confirmations

4,997,551

Mined by

⛏️ P2SHAJFHyZVarsRQXFPwJ1GMAQKBrYbq2Y2xCT

Merkle Root

ba357ce647d48b78ab2c145bd7eb40924ce633ad4d130f13ed3460f29bc057c4
Transactions (1)
Coinbaseba357ce647d48b…3460f29bc057c4
1 in β†’ 1 out8.8700 XPM110 B
AJFHyZVa…bq2Y2xCT
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.

1.069 Γ— 10⁹⁷(98-digit number)
10691956177267398662…56951657870431662079
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
1.069 Γ— 10⁹⁷(98-digit number)
10691956177267398662…56951657870431662079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.069 Γ— 10⁹⁷(98-digit number)
10691956177267398662…56951657870431662081
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
2.138 Γ— 10⁹⁷(98-digit number)
21383912354534797325…13903315740863324159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.138 Γ— 10⁹⁷(98-digit number)
21383912354534797325…13903315740863324161
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
4.276 Γ— 10⁹⁷(98-digit number)
42767824709069594650…27806631481726648319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.276 Γ— 10⁹⁷(98-digit number)
42767824709069594650…27806631481726648321
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
8.553 Γ— 10⁹⁷(98-digit number)
85535649418139189300…55613262963453296639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.553 Γ— 10⁹⁷(98-digit number)
85535649418139189300…55613262963453296641
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
1.710 Γ— 10⁹⁸(99-digit number)
17107129883627837860…11226525926906593279
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.710 Γ— 10⁹⁸(99-digit number)
17107129883627837860…11226525926906593281
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
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