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Block #1,105,371

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/14/2015, 11:45:40 PM Β· Difficulty 10.7811 Β· 5,703,186 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
75fab5962dbdec2c50b3e8b5e8aaa11de478b6b538708aa3d4019a94b7545e77
View on Chainz β†—

Height

#1,105,371

Difficulty

10.781080

Transactions

2

Size

1.68 KB

Version

2

Bits

0ac7f4db

Nonce

58,024,608

Timestamp

6/14/2015, 11:45:40 PM

Confirmations

5,703,186

Mined by

⛏️ P2SHAaC8y4igkMpsDzWAZ36FFNiz3Tq4ove18i

Merkle Root

2777975aba30b993287712046c58fd24f54d7327e66690d83e0b2f2440221247
Transactions (2)
Coinbasebd5d333996fb8d…1b7436b00c6eb1
1 in β†’ 1 out8.6100 XPM109 B
AaC8y4ig…q4ove18i
a423c1c0e4d270…11c8c27fd65361
10 in β†’ 1 out3.7502 XPM1.49 KB
AVYjNJEW…jTeas9v4
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.

1.105 Γ— 10⁹⁴(95-digit number)
11052734210408241116…58583736603496522239
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
1.105 Γ— 10⁹⁴(95-digit number)
11052734210408241116…58583736603496522239
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.105 Γ— 10⁹⁴(95-digit number)
11052734210408241116…58583736603496522241
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
2.210 Γ— 10⁹⁴(95-digit number)
22105468420816482232…17167473206993044479
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.210 Γ— 10⁹⁴(95-digit number)
22105468420816482232…17167473206993044481
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
4.421 Γ— 10⁹⁴(95-digit number)
44210936841632964465…34334946413986088959
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.421 Γ— 10⁹⁴(95-digit number)
44210936841632964465…34334946413986088961
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
8.842 Γ— 10⁹⁴(95-digit number)
88421873683265928930…68669892827972177919
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.842 Γ— 10⁹⁴(95-digit number)
88421873683265928930…68669892827972177921
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
1.768 Γ— 10⁹⁡(96-digit number)
17684374736653185786…37339785655944355839
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.768 Γ— 10⁹⁡(96-digit number)
17684374736653185786…37339785655944355841
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:57,712,513 XPMΒ·at block #6,808,556 Β· updates every 60s
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