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Block #1,288,372

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 10/19/2015, 8:24:40 AM Β· Difficulty 10.8312 Β· 5,529,009 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
6c88887091b5c508decd0e42b1020c89c59c4a015ce899d1fa11022129209dba
View on Chainz β†—

Height

#1,288,372

Difficulty

10.831218

Transactions

2

Size

20.94 KB

Version

2

Bits

0ad4caae

Nonce

1,397,516,553

Timestamp

10/19/2015, 8:24:40 AM

Confirmations

5,529,009

Mined by

⛏️ P2SHAGJL6k9KE5HfPTYjSW1wmWQrsCQQocPDXo

Merkle Root

8dba9248e41f8868d71881b5794d9f5ea47a7ea915a72190decd73bd0c6e3599
Transactions (2)
Coinbase2fc89b0ecbfb72…395d2818311331
1 in β†’ 1 out8.8100 XPM109 B
AGJL6k9K…QQocPDXo
62061e9e6d07b0…ac36b3d43fab8c
143 in β†’ 2 out432.0094 XPM20.75 KB
ALKM4Br8…YVqfPiBXAH1uQGkX…e259KUsM
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.

1.932 Γ— 10⁹⁴(95-digit number)
19329171368217905255…57951911745716765959
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
1.932 Γ— 10⁹⁴(95-digit number)
19329171368217905255…57951911745716765959
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.932 Γ— 10⁹⁴(95-digit number)
19329171368217905255…57951911745716765961
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
3.865 Γ— 10⁹⁴(95-digit number)
38658342736435810511…15903823491433531919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.865 Γ— 10⁹⁴(95-digit number)
38658342736435810511…15903823491433531921
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
7.731 Γ— 10⁹⁴(95-digit number)
77316685472871621022…31807646982867063839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.731 Γ— 10⁹⁴(95-digit number)
77316685472871621022…31807646982867063841
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
1.546 Γ— 10⁹⁡(96-digit number)
15463337094574324204…63615293965734127679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.546 Γ— 10⁹⁡(96-digit number)
15463337094574324204…63615293965734127681
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
3.092 Γ— 10⁹⁡(96-digit number)
30926674189148648409…27230587931468255359
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.092 Γ— 10⁹⁡(96-digit number)
30926674189148648409…27230587931468255361
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
6.185 Γ— 10⁹⁡(96-digit number)
61853348378297296818…54461175862936510719
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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