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Block #1,071,869

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/23/2015, 6:49:37 AM Β· Difficulty 10.7420 Β· 5,731,780 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
48cf27ea0928a08275350122d0329bc95c806706cd0d66739471685c0a382209
View on Chainz β†—

Height

#1,071,869

Difficulty

10.741955

Transactions

2

Size

59.68 KB

Version

2

Bits

0abdf0c2

Nonce

287,178,855

Timestamp

5/23/2015, 6:49:37 AM

Confirmations

5,731,780

Mined by

⛏️ P2SHAX7824uhxbFDyAEoBdTKXnGQXhLx5Yfv2R

Merkle Root

5824a7c9000ef8ffaaf6eeb387b85d63996ab937ead0d5f305130f6e0fc3d450
Transactions (2)
Coinbase4b0c89689f684b…3fcd70d5ed4313
1 in β†’ 1 out9.3800 XPM109 B
AX7824uh…Lx5Yfv2R
45742eb5e36112…1c6b4fbfa9f02c
411 in β†’ 2 out24434.0727 XPM59.49 KB
AQ5KT526…tGengjpEAabZeMM7…hdLbBfGN
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.

4.730 Γ— 10⁹⁡(96-digit number)
47308802489641880426…86522989128821996799
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
4.730 Γ— 10⁹⁡(96-digit number)
47308802489641880426…86522989128821996799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.730 Γ— 10⁹⁡(96-digit number)
47308802489641880426…86522989128821996801
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
9.461 Γ— 10⁹⁡(96-digit number)
94617604979283760853…73045978257643993599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.461 Γ— 10⁹⁡(96-digit number)
94617604979283760853…73045978257643993601
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
1.892 Γ— 10⁹⁢(97-digit number)
18923520995856752170…46091956515287987199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.892 Γ— 10⁹⁢(97-digit number)
18923520995856752170…46091956515287987201
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
3.784 Γ— 10⁹⁢(97-digit number)
37847041991713504341…92183913030575974399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.784 Γ— 10⁹⁢(97-digit number)
37847041991713504341…92183913030575974401
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
7.569 Γ— 10⁹⁢(97-digit number)
75694083983427008683…84367826061151948799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.569 Γ— 10⁹⁢(97-digit number)
75694083983427008683…84367826061151948801
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
1.513 Γ— 10⁹⁷(98-digit number)
15138816796685401736…68735652122303897599
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:57,673,225 XPMΒ·at block #6,803,648 Β· updates every 60s
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