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Block #1,595,200

TWNLength 10ā˜…ā˜…ā˜†ā˜†ā˜†

Bi-Twin Chain Ā· Discovered 5/22/2016, 10:06:23 AM Ā· Difficulty 10.6228 Ā· 5,243,977 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e910eb7b4a4dd34b66c27df616eea594603af99dc3a7091d6e8a933f21a90c73
View on Chainz ā†—

Height

#1,595,200

Difficulty

10.622777

Transactions

2

Size

1.11 KB

Version

2

Bits

0a9f6e4c

Nonce

879,528,528

Timestamp

5/22/2016, 10:06:23 AM

Confirmations

5,243,977

Mined by

ā›ļø P2SHAQ8At2r7qhN85eBWwYRNrRnRAU8Mj9FA28

Merkle Root

bfef6e5f2f42c6e90fd5d07b0cd89d9e2f93a5dbbec192ebfcf8a84e0b4b6a9a
Transactions (2)
Coinbase1f7fe43633766cā€¦d9c9a0f33fe43c
1 in ā†’ 1 out8.8600 XPM109 B
AQ8At2r7ā€¦8Mj9FA28
5f689ce624f631ā€¦272c3e0ba45748
1 in ā†’ 23 out58.0464 XPM941 B
AcJzrqoNā€¦sC5CU1nwAGk5qbCsā€¦DAwM1uXaASwncKHmā€¦gjcC3SkfAcFXYrqLā€¦eZs2e3RrAL9VEYnRā€¦4vRHwUx2
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) ā€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

5.314 Ɨ 10ā¹ā“(95-digit number)
53143038090939936446ā€¦63189384787008237759
Discovered Prime Numbers
Lower: 2^k Ɨ origin āˆ’ 1 | Upper: 2^k Ɨ 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 ā€” Twin Prime Pair (origin Ā± 1)
origin āˆ’ 1
5.314 Ɨ 10ā¹ā“(95-digit number)
53143038090939936446ā€¦63189384787008237759
Verify on FactorDB ā†—Wolfram Alpha ā†—
origin + 1
5.314 Ɨ 10ā¹ā“(95-digit number)
53143038090939936446ā€¦63189384787008237761
Verify on FactorDB ā†—Wolfram Alpha ā†—
Difference: origin + 1 āˆ’ origin āˆ’ 1 = 2 (twin primes āœ“)
Level 1 ā€” Twin Prime Pair (2^1 Ɨ origin Ā± 1)
2^1 Ɨ origin āˆ’ 1
1.062 Ɨ 10ā¹āµ(96-digit number)
10628607618187987289ā€¦26378769574016475519
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^1 Ɨ origin + 1
1.062 Ɨ 10ā¹āµ(96-digit number)
10628607618187987289ā€¦26378769574016475521
Verify on FactorDB ā†—Wolfram Alpha ā†—
Difference: 2^1 Ɨ origin + 1 āˆ’ 2^1 Ɨ origin āˆ’ 1 = 2 (twin primes āœ“)
Level 2 ā€” Twin Prime Pair (2^2 Ɨ origin Ā± 1)
2^2 Ɨ origin āˆ’ 1
2.125 Ɨ 10ā¹āµ(96-digit number)
21257215236375974578ā€¦52757539148032951039
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^2 Ɨ origin + 1
2.125 Ɨ 10ā¹āµ(96-digit number)
21257215236375974578ā€¦52757539148032951041
Verify on FactorDB ā†—Wolfram Alpha ā†—
Difference: 2^2 Ɨ origin + 1 āˆ’ 2^2 Ɨ origin āˆ’ 1 = 2 (twin primes āœ“)
Level 3 ā€” Twin Prime Pair (2^3 Ɨ origin Ā± 1)
2^3 Ɨ origin āˆ’ 1
4.251 Ɨ 10ā¹āµ(96-digit number)
42514430472751949156ā€¦05515078296065902079
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^3 Ɨ origin + 1
4.251 Ɨ 10ā¹āµ(96-digit number)
42514430472751949156ā€¦05515078296065902081
Verify on FactorDB ā†—Wolfram Alpha ā†—
Difference: 2^3 Ɨ origin + 1 āˆ’ 2^3 Ɨ origin āˆ’ 1 = 2 (twin primes āœ“)
Level 4 ā€” Twin Prime Pair (2^4 Ɨ origin Ā± 1)
2^4 Ɨ origin āˆ’ 1
8.502 Ɨ 10ā¹āµ(96-digit number)
85028860945503898313ā€¦11030156592131804159
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^4 Ɨ origin + 1
8.502 Ɨ 10ā¹āµ(96-digit number)
85028860945503898313ā€¦11030156592131804161
Verify on FactorDB ā†—Wolfram Alpha ā†—
Difference: 2^4 Ɨ origin + 1 āˆ’ 2^4 Ɨ origin āˆ’ 1 = 2 (twin primes āœ“)

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 ā€” the large number shown above ā€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

ā˜…ā˜…ā˜†ā˜†ā˜†
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 Ɨ 3 Ɨ 5 Ɨ 7 Ɨ ā€¦), the result is the first prime in the chain. The origin is deliberately divisible by this primorial ā€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Ɨ Primorial (2Ā·3Ā·5Ā·7Ā·11Ā·ā€¦)
Source: Primecoin prime.cpp ā€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors ā€” 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 āˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,957,698 XPMĀ·at block #6,839,176 Ā· updates every 60s
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