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Block #2,758,858

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 7/21/2018, 12:26:44 PM Β· Difficulty 11.6639 Β· 4,085,044 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f732d9c2c06e1fffc3fabd75c8b41c97cc22a20ee4125b6bc5c1938204857e4b
View on Chainz β†—

Height

#2,758,858

Difficulty

11.663876

Transactions

2

Size

572 B

Version

2

Bits

0ba9f3cc

Nonce

1,508,230,491

Timestamp

7/21/2018, 12:26:44 PM

Confirmations

4,085,044

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

b0fc11997477c18e5b11fb8ec829fa4e91768dffc8795f61d3cae8c6d5e79481
Transactions (2)
Coinbase61ed54956e746e…0461073e3d25b8
1 in β†’ 1 out7.3500 XPM110 B
AZtxQr2F…7grUWrUz
b789e463d12583…b2928fc7f58d6b
2 in β†’ 2 out7.9900 XPM373 B
AKiMeRLV…6vUcMAG9AdJydtgN…ctLN5Ur7
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.

1.572 Γ— 10⁹³(94-digit number)
15726029161697395596…28299892051254649299
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
1.572 Γ— 10⁹³(94-digit number)
15726029161697395596…28299892051254649299
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.572 Γ— 10⁹³(94-digit number)
15726029161697395596…28299892051254649301
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
3.145 Γ— 10⁹³(94-digit number)
31452058323394791193…56599784102509298599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.145 Γ— 10⁹³(94-digit number)
31452058323394791193…56599784102509298601
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
6.290 Γ— 10⁹³(94-digit number)
62904116646789582386…13199568205018597199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.290 Γ— 10⁹³(94-digit number)
62904116646789582386…13199568205018597201
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
1.258 Γ— 10⁹⁴(95-digit number)
12580823329357916477…26399136410037194399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.258 Γ— 10⁹⁴(95-digit number)
12580823329357916477…26399136410037194401
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
2.516 Γ— 10⁹⁴(95-digit number)
25161646658715832954…52798272820074388799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.516 Γ— 10⁹⁴(95-digit number)
25161646658715832954…52798272820074388801
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
5.032 Γ— 10⁹⁴(95-digit number)
50323293317431665909…05596545640148777599
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:57,995,587 XPMΒ·at block #6,843,901 Β· updates every 60s
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