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Block #2,335,114

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 10/13/2017, 11:28:32 AM Β· Difficulty 10.9205 Β· 4,498,622 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
62c5e1f8d528ab75f333a3c9bfec7af2d8af8e73d1640fdf42e6c22b31892696
View on Chainz β†—

Height

#2,335,114

Difficulty

10.920545

Transactions

2

Size

424 B

Version

2

Bits

0aeba8dd

Nonce

2,067,579,414

Timestamp

10/13/2017, 11:28:32 AM

Confirmations

4,498,622

Mined by

⛏️ P2SHAa1JeNsRtXbso3thbpbrqDu4QzeJpopRVv

Merkle Root

8c580eef5742439498bacb76cfaa920d0e596baf6473db4798f6173fc35d9e4c
Transactions (2)
Coinbaseb71fd93bcf88aa…c41c3c3b677442
1 in β†’ 1 out8.3800 XPM109 B
Aa1JeNsR…eJpopRVv
e705fc6a3149a0…c2b6c0dac50b48
1 in β†’ 2 out99999.9900 XPM225 B
AH23bBDK…9B3J8zuzAS5zPLa1…MhwfAkTZ
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.

1.199 Γ— 10⁹⁴(95-digit number)
11996989494818779435…15827782862886135999
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
1.199 Γ— 10⁹⁴(95-digit number)
11996989494818779435…15827782862886135999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.199 Γ— 10⁹⁴(95-digit number)
11996989494818779435…15827782862886136001
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
2.399 Γ— 10⁹⁴(95-digit number)
23993978989637558871…31655565725772271999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.399 Γ— 10⁹⁴(95-digit number)
23993978989637558871…31655565725772272001
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
4.798 Γ— 10⁹⁴(95-digit number)
47987957979275117742…63311131451544543999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.798 Γ— 10⁹⁴(95-digit number)
47987957979275117742…63311131451544544001
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
9.597 Γ— 10⁹⁴(95-digit number)
95975915958550235484…26622262903089087999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.597 Γ— 10⁹⁴(95-digit number)
95975915958550235484…26622262903089088001
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
1.919 Γ— 10⁹⁡(96-digit number)
19195183191710047096…53244525806178175999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.919 Γ— 10⁹⁡(96-digit number)
19195183191710047096…53244525806178176001
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
3.839 Γ— 10⁹⁡(96-digit number)
38390366383420094193…06489051612356351999
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
Circulating Supply:57,914,105 XPMΒ·at block #6,833,735 Β· updates every 60s
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