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Block #1,433,296

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/28/2016, 6:02:11 PM Β· Difficulty 10.7964 Β· 5,411,319 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a847ce0193a3dcb703664e5448c8a48b1aeb517554a681d8258cab44d058d6d2
View on Chainz β†—

Height

#1,433,296

Difficulty

10.796410

Transactions

1

Size

200 B

Version

2

Bits

0acbe18b

Nonce

534,496,872

Timestamp

1/28/2016, 6:02:11 PM

Confirmations

5,411,319

Mined by

⛏️ P2SHAZfNrbB6KeNAyKog2Yen8idqPJEuCEwUu6

Merkle Root

c844ebc84e8eef532c7616469d9f71ddcdcae9b6bf8e1958e53eea71acaeed82
Transactions (1)
Coinbasec844ebc84e8eef…3eea71acaeed82
1 in β†’ 1 out8.5700 XPM110 B
AZfNrbB6…EuCEwUu6
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.

5.445 Γ— 10⁹⁴(95-digit number)
54455166431258581852…78691841204181094399
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
5.445 Γ— 10⁹⁴(95-digit number)
54455166431258581852…78691841204181094399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.445 Γ— 10⁹⁴(95-digit number)
54455166431258581852…78691841204181094401
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
1.089 Γ— 10⁹⁡(96-digit number)
10891033286251716370…57383682408362188799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.089 Γ— 10⁹⁡(96-digit number)
10891033286251716370…57383682408362188801
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
2.178 Γ— 10⁹⁡(96-digit number)
21782066572503432740…14767364816724377599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.178 Γ— 10⁹⁡(96-digit number)
21782066572503432740…14767364816724377601
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
4.356 Γ— 10⁹⁡(96-digit number)
43564133145006865481…29534729633448755199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.356 Γ— 10⁹⁡(96-digit number)
43564133145006865481…29534729633448755201
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
8.712 Γ— 10⁹⁡(96-digit number)
87128266290013730963…59069459266897510399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.712 Γ— 10⁹⁡(96-digit number)
87128266290013730963…59069459266897510401
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:58,001,324 XPMΒ·at block #6,844,614 Β· updates every 60s
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