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Block #817,734

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/19/2014, 1:11:12 AM Β· Difficulty 10.9760 Β· 5,997,402 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
9e1d4946fc1ea46958f823088f512d62d4a058429edd2d703bff947643362ff3
View on Chainz β†—

Height

#817,734

Difficulty

10.975963

Transactions

1

Size

242 B

Version

2

Bits

0af9d8ae

Nonce

603,163,602

Timestamp

11/19/2014, 1:11:12 AM

Confirmations

5,997,402

Mined by

⛏️ jhPrimeminerAYFivgcJEqUfH1zEbfNs35USz3FT8wELGF

Merkle Root

ddebe3db575e024b544d2b087d7bb1d6f6fc4abc8006d7bb9841865e4d1d9454
Transactions (1)
Coinbaseddebe3db575e02…41865e4d1d9454
1 in β†’ 2 out8.2900 XPM152 B
AYFivgcJ…FT8wELGFALPu3s2c…EJXLjVFh
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.

2.839 Γ— 10⁹⁡(96-digit number)
28390068909706349325…04968380401817284799
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
2.839 Γ— 10⁹⁡(96-digit number)
28390068909706349325…04968380401817284799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.839 Γ— 10⁹⁡(96-digit number)
28390068909706349325…04968380401817284801
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
5.678 Γ— 10⁹⁡(96-digit number)
56780137819412698650…09936760803634569599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.678 Γ— 10⁹⁡(96-digit number)
56780137819412698650…09936760803634569601
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
1.135 Γ— 10⁹⁢(97-digit number)
11356027563882539730…19873521607269139199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.135 Γ— 10⁹⁢(97-digit number)
11356027563882539730…19873521607269139201
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
2.271 Γ— 10⁹⁢(97-digit number)
22712055127765079460…39747043214538278399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.271 Γ— 10⁹⁢(97-digit number)
22712055127765079460…39747043214538278401
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
4.542 Γ— 10⁹⁢(97-digit number)
45424110255530158920…79494086429076556799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.542 Γ— 10⁹⁢(97-digit number)
45424110255530158920…79494086429076556801
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:57,765,181 XPMΒ·at block #6,815,135 Β· updates every 60s
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