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Block #851,630

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 12/13/2014, 11:11:49 AM Β· Difficulty 10.9704 Β· 5,982,292 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1ee98c4ef5dab27692ad7a762084ff90dca2777c690a799239bdb5ca9fe44b8a
View on Chainz β†—

Height

#851,630

Difficulty

10.970417

Transactions

3

Size

806 B

Version

2

Bits

0af86d39

Nonce

99,960,448

Timestamp

12/13/2014, 11:11:49 AM

Confirmations

5,982,292

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

869a23eee9e7eb89d8c60d6f1cafc9e8922d60dff1135aa9f3e2c5bbc88c1ef1
Transactions (3)
Coinbase723cd87728aa2a…4fd7e7654c6bd5
1 in β†’ 1 out8.3332 XPM116 B
ANSXnLY2…Sd25TjkD
4d4d17acba8dd8…9c009c19664205
1 in β†’ 3 out0.2306 XPM259 B
AdqVKi4U…g9drbR8UAK6an6xE…KLiR7JrqAey8QtnV…u2E8D2mL
f7516abf5bcea4…9438d5e4fab882
2 in β†’ 1 out0.0105 XPM340 B
AQ3Y3x6r…BSKm1ifA
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.

9.774 Γ— 10⁹⁡(96-digit number)
97745156094458571040…97662112186042444799
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
9.774 Γ— 10⁹⁡(96-digit number)
97745156094458571040…97662112186042444799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.774 Γ— 10⁹⁡(96-digit number)
97745156094458571040…97662112186042444801
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
1.954 Γ— 10⁹⁢(97-digit number)
19549031218891714208…95324224372084889599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.954 Γ— 10⁹⁢(97-digit number)
19549031218891714208…95324224372084889601
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
3.909 Γ— 10⁹⁢(97-digit number)
39098062437783428416…90648448744169779199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.909 Γ— 10⁹⁢(97-digit number)
39098062437783428416…90648448744169779201
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
7.819 Γ— 10⁹⁢(97-digit number)
78196124875566856832…81296897488339558399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.819 Γ— 10⁹⁢(97-digit number)
78196124875566856832…81296897488339558401
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
1.563 Γ— 10⁹⁷(98-digit number)
15639224975113371366…62593794976679116799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.563 Γ— 10⁹⁷(98-digit number)
15639224975113371366…62593794976679116801
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
3.127 Γ— 10⁹⁷(98-digit number)
31278449950226742732…25187589953358233599
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
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