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Block #2,873,443

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 10/9/2018, 2:56:01 AM Β· Difficulty 11.6651 Β· 3,963,479 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ec3d5d819e8ab63a7439bd86f4d73197c4a144369a610ca1ffe5785359048711
View on Chainz β†—

Height

#2,873,443

Difficulty

11.665119

Transactions

2

Size

4.32 KB

Version

2

Bits

0baa4539

Nonce

382,791,551

Timestamp

10/9/2018, 2:56:01 AM

Confirmations

3,963,479

Mined by

⛏️ P2SHAMSLb8igZbgt9yjR1nQcr7khPhy44kgrZP

Merkle Root

4338aaa98cc5c4eca29bbc23b77034d9004d79fe91abc111985ec850a7196f39
Transactions (2)
Coinbased00a1a18f64bdc…f21e13f3c904a4
1 in β†’ 1 out7.4000 XPM110 B
AMSLb8ig…y44kgrZP
c60152291fbd1a…45d18eca5a2d8d
28 in β†’ 2 out1166.9955 XPM4.12 KB
AV3aP88j…YwWaa9qKAT2ZqrhV…zrdzQgZb
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.

1.024 Γ— 10⁹⁷(98-digit number)
10248697419502856738…95198702475052646399
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
1.024 Γ— 10⁹⁷(98-digit number)
10248697419502856738…95198702475052646399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.024 Γ— 10⁹⁷(98-digit number)
10248697419502856738…95198702475052646401
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
2.049 Γ— 10⁹⁷(98-digit number)
20497394839005713476…90397404950105292799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.049 Γ— 10⁹⁷(98-digit number)
20497394839005713476…90397404950105292801
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
4.099 Γ— 10⁹⁷(98-digit number)
40994789678011426952…80794809900210585599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.099 Γ— 10⁹⁷(98-digit number)
40994789678011426952…80794809900210585601
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
8.198 Γ— 10⁹⁷(98-digit number)
81989579356022853904…61589619800421171199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.198 Γ— 10⁹⁷(98-digit number)
81989579356022853904…61589619800421171201
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
1.639 Γ— 10⁹⁸(99-digit number)
16397915871204570780…23179239600842342399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.639 Γ— 10⁹⁸(99-digit number)
16397915871204570780…23179239600842342401
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
3.279 Γ— 10⁹⁸(99-digit number)
32795831742409141561…46358479201684684799
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:57,939,671 XPMΒ·at block #6,836,921 Β· updates every 60s
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